CN108880383B - Discretization design method for proportional resonant controller of permanent magnet motor - Google Patents

Abstract

The invention discloses a discretization design method for a proportional resonance controller of a permanent magnet motor. Discrete model; in the synchronous sampling mode, the output of the controller has a delay of one sampling period. In order to include the delay of one sampling period in the discrete model, the state space expression is expanded to obtain the open-loop model of the current control system; The integrator eliminates the steady-state error, and deduces the closed-loop model of the current control system combined with the state feedback control structure; determines the desired zero-pole point of the current-control closed-loop system, uses the direct zero-pole configuration method to set the current controller parameters, and determines the current control system according to the parameter setting method. The online calculation method of controller parameters is used to meet the needs of online calculation of current controller parameters. The invention improves the stability and control precision of the motor current loop control system.

Description

Discrete Design Method of Proportional Resonance Controller for Permanent Magnet Motor

technical field

The invention relates to the field of electrical transmission, in particular to a discrete design method of a proportional resonance controller in a permanent magnet motor digital control system.

Background technique

The current closed-loop control is a basic link of the motor control system. The dynamic response and control accuracy of the current loop directly affect the overall performance of the motor control system. In the flux-oriented control mode, the current loop of the permanent magnet motor control system usually adopts a control scheme based on coordinate transformation. At this time, the computational burden of the control system is heavy, and the control structure is relatively complex, especially in applications that need to suppress harmonics. Therefore, in order to reduce the computational burden, some scholars have proposed a control scheme using a proportional resonant controller in a stationary coordinate system.

The proportional resonant controller can simultaneously track both positive and negative sequence AC signals at a specified frequency with no error in steady state. Therefore, proportional resonant controllers are widely used in grid-connected inverters, active power filters and motor drive systems ^[1-3] . The design method of proportional resonant controller usually adopts the continuous design method.

The continuous design method usually designs the controller based on the transfer function, and then obtains the digital controller through the discretization method. In this method, the output delay of the controller in the digital control system is taken as one sampling period, and the zero-order hold characteristic of the PWM link is equivalent to the delay of 0.5 times the sampling period ^[4] . This equivalent method cannot accurately reflect the discrete characteristics of the digital control system, and it is difficult to ensure the stability of the control system when the switching frequency is low.

In practical applications, the choice of discretization method greatly affects the control performance. Moreover, the influence of different discretization methods on controller performance is reflected in different aspects, which increases the difficulty of controller design ^[5] . Therefore, the continuous design method of proportional resonance controller is difficult to ensure the stability and control accuracy of the control system.

references

[1]Timbus A,Liserre M,Teodorescu R,et al.Evaluation of CurrentControllers for Distributed Power Generation Systems[J].IEEE Transactions onPower Electronics,2009,24(3):654-664.

[2] Yuan X, Merk W, Stemmler H, et al. Stationary-frame generalized integrators for current control of active power filters with zero steady-state error for current harmonics of concern under unbalanced and distortedoperating conditions[J].IEEE Transactions on Industry Applications, 2002, 38(2): 523-532.

[3]Chou M C,Liaw C M.Development of Robust Current 2-DOF Controllers for a Permanent Magnet Synchronous Motor Drive With Reaction Wheel Load[J].IEEE Transactions on Power Electronics,2009,24(5):1304-1320.

[4]Holmes D G, Lipo T A, Mcgrath B P, et al.Optimized Design of Stationary Frame Three Phase AC Current Regulators[J].IEEE Transactions onPower Electronics,2009,24(11):2417-2426.

[5] Yepes A G, Freijedo F D, Doval-Gandoy J, et al. Effects of Discretization Methods on the Performance of ResonantControllers [J]. IEEE Transactions on Power Electronics, 2010, 25(7): 1692-1712.

SUMMARY OF THE INVENTION

The invention provides a discrete design method for a proportional resonance controller of a permanent magnet motor. The invention takes into account the sampling, delay and zero-order hold characteristics of PWM existing in a digital control system. The invention uses a direct pole configuration method to control the current. The parameter setting of the controller improves the stability and control accuracy of the motor current loop control system. See the description below for details:

A discretized design method for a proportional resonance controller of a permanent magnet motor, the method comprises the following steps:

Considering the sampling and zero-order hold characteristics of PWM in the digital control system, the continuous model of the motor current loop is discretized, and the discrete model is obtained;

In the synchronous sampling mode, the output of the controller has a delay of one sampling period. In order to include the delay of one sampling period in the discrete model, the state space expression is expanded to obtain the open-loop model of the current control system;

An integrator is introduced to eliminate the steady-state error, and the closed-loop model of the current control system is derived by combining the state feedback control structure;

Determine the expected zero and pole of the current control closed-loop system, use the direct zero-pole configuration method to set the current controller parameters, and determine the online calculation method of the current controller parameters according to the parameter setting method to meet the needs of the online calculation of the current controller parameters.

Further, the method further includes: establishing a continuous model of the current loop of the permanent magnet motor.

Wherein, the introduction of the integrator to eliminate the steady-state error, combined with the state feedback control structure to deduce the closed-loop model of the current control system is as follows:

A feedback channel including an integrator is added to the state feedback control, and the introduction of the integral adds two integral states to obtain the corresponding difference equation;

Add the integral state to the difference equation to get the expression after the expansion state;

The control law is obtained from the state feedback control structure, and then the closed-loop model of the current control system is derived.

Further, the corresponding difference equation is:

x _I1 (k+1)=x _I2 (k)

x _I2 (k+1)=-x _I1 (k)+2cos(ω ₀ T _s )x _I2 (k)+H _d x _d (k)-i _ref (k)

Among them, i _ref (k) is the sampling value of the given current; ω ₀ is the angular frequency of the given current.

During specific implementation, the expression after the expanded state is specifically:

Among them, x _a (k) is the expanded state variable matrix, and Φ _a , Γ _ca , Γ _ra and Γ _ea are used to represent the expanded parameter matrix.

Further, the control law is:

Among them, Ka is used to represent the state feedback gain matrix after the expanded state; KN _{x is} the given feedforward gain.

Further, the closed-loop model of the current control system is:

x _a (k+1)=(Φ _a -Γ _ca K _a )x _a (k)+(Γ _ra +Γ _ca KN _x )i _ref (k)+Γ _ea u _e (k)

i(k)=H _a x _a (k)

In the formula, the output matrix H _a =[1 0 0 0].

The specific parameter setting of the current controller using the direct zero-pole configuration method is as follows:

There are two open-loop poles in the current control system, which are respectively introduced by the time delay and the controlled object. The pole introduced by the time delay is located at the origin, and the pole introduced by the controlled object is located at the origin.

和

The two complex poles introduced by the integrator are chosen as the dominant poles, and the last real pole remains fixed and canceled by a zero; the desired four poles are set to 0, respectively,

and

消除实数极点，电流控制器前馈系数由这个零点确定；主导极点为电流控制器引入的一对复极点，其位置由电流控制闭环系统的设计要求确定。A zero is set to

The real number pole is eliminated, and the feedforward coefficient of the current controller is determined by this zero point; the dominant pole is a pair of complex poles introduced by the current controller, and its position is determined by the design requirements of the current control closed-loop system.

Further, the method also includes:

The gain of the current controller can be written as an analytical formula about the parameters of the current control system and the configured closed-loop zero-pole. Based on this, the current controller can perform parameter self-tuning.

The beneficial effects of the technical scheme provided by the present invention are:

1. This method fully considers the sampling, delay and zero-order hold characteristics of PWM existing in the digital control system. Compared with the continuous design method in the prior art, the stability and control accuracy of the current closed-loop system are improved;

2. The desired dynamic performance of the current closed-loop system in this method can be directly obtained by configuring the corresponding closed-loop poles and zeros;

3. The current controller coefficients in this method can be calculated online, and when the parameters of the controlled object change, the current closed-loop system can recalculate the controller parameters, which has higher adaptability.

Description of drawings

Fig. 1 is a state feedback control block diagram with an integrator;

为反电动势的估计值。电流实际值和电流给定的误差作为积分器的输入，积分器的输出由积分状态X_I和积分增益K_I共同确定。电流控制器的输出包含了积分器输出、给定的前馈、电流闭环系统状态的反馈和干扰的估计值。In the figure, ω ₀ is the angular frequency given by the current, T _s is the sampling period,

is the estimated value of the back EMF. The current actual value and the error given by the current are used as the input of the integrator, and the output of the integrator is jointly determined by the integration state X _I and the integration gain K _I. The output of the current controller contains the integrator output, the given feedforward, the feedback of the current closed-loop system state, and an estimate of the disturbance.

Figure 2 is a block diagram of a current closed-loop system;

表示反电动势的估计值，系数T表示2cos(ω₀T_s)。电流控制器的输出经过限幅和延时作为调制环节的输入。1/KN_x表示电流控制器抑制积分饱和策略的反计算增益。Among them, the gray background in the figure represents the actual system of the current loop, and the white background represents the digital controller.

represents the estimated value of the back EMF, and the coefficient T represents 2cos(ω ₀ T _s ). The output of the current controller is limited and delayed as the input of the modulation link. 1/KN _x represents the inverse calculation gain of the current controller to suppress the integral saturation strategy.

Figure 3 is a schematic diagram of the open-loop zero-pole distribution;

Among them, the poles in the figure are represented by '×', and the zeros are represented by '○'.

Figure 4 is a schematic diagram of closed-loop zero-pole distribution;

Among them, the poles in the figure are represented by '×', and the zeros are represented by '○'.

Fig. 5 is the flow chart of the online calculation of the parameters of the current loop proportional resonance controller.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention are further described in detail below.

In the design process of the current controller, the method of the equivalent PWM zero-order holding characteristic of the delay link cannot accurately reflect the discrete characteristic of the digital control system. The quality of control performance also depends on the choice of discretization method. In order to overcome the above drawbacks, an embodiment of the present invention proposes a discrete design method for a proportional resonance controller of a permanent magnet motor.

Example 1

A discretized design method for a proportional resonance controller of a permanent magnet motor, see Figure 1, the method includes the following steps:

101: Establish a continuous model of the current loop of the permanent magnet motor;

102: Considering the sampling and zero-order hold characteristics of PWM existing in the digital control system, discretize the continuous model of the motor current loop to obtain a discrete model;

103: In the synchronous sampling mode, the output of the controller has a delay of one sampling period. In order to include the delay of one sampling period in the discrete model, the state space expression is expanded to obtain an open-loop model of the current control system;

104: Introduce an integrator to eliminate the steady-state error, and derive a closed-loop model of the current control system combined with the state feedback control structure;

105: Determine the expected zero-pole point of the current control closed-loop system, use the direct zero-pole configuration method to set the parameters of the current controller, and determine the online calculation method of the current controller parameters according to the parameter setting method, so as to meet the needs of the online calculation of the current controller parameters.

To sum up, in the embodiment of the present invention, the sampling, delay and zero-order hold characteristics of PWM existing in the digital control system are considered through the above steps 101 to 105, and the direct pole configuration method is used to adjust the parameters of the current controller, so as to improve the performance of the current controller. The stability and control accuracy of the motor current loop control system are improved.

Example 2

The scheme in Embodiment 1 is further introduced below in conjunction with specific calculation formulas and examples, and is described in detail below:

1. Discrete design method of proportional resonant controller

Different from the direct current component in the synchronous rotating coordinate system, the stator current in the αβ axis component in the two-phase stationary coordinate system is still the alternating current. In order to realize the static-free control of the current, the current controller needs to provide infinite gain to the AC signal of the specified frequency, so the proportional resonance controller is selected as the current controller. In addition, in order to simplify the design process, the design of this current controller is analyzed using complex vectors, and complex numbers, matrices and vectors are all represented in bold.

1. Establish a continuous model of the current loop

As the basis for studying the discrete model of the current loop of the permanent magnet motor, the continuous mathematical model of the current loop in the two-phase stationary αβ system is established first. The stator resistance and synchronous inductance of the permanent magnet motor are represented by R _f and L _f respectively, and these two physical quantities are regarded as the controlled objects of the current loop of the permanent magnet motor. The stator current vector and stator voltage vector are denoted by i and _uc , respectively. The induced electromotive force is regarded as disturbance and represented by _ue . The induced electromotive force may be obtained by an observer or other methods, and the estimation method thereof is not discussed in this embodiment of the present invention.

Using the state differential equation and the output equation, the dynamic characteristics of the permanent magnet motor current loop can be expressed as:

i=x

In the formula, i=i _α +ji _β , u _c =u _cα +ju _cβ , _ue =u _eα +ju _eβ .

Among them, x is the state variable of the continuous current loop system; i _α is the component of the stator current vector i on the α axis; i _β is the component of the stator current vector i on the β axis; j is the imaginary unit; u _cα is the stator The component of the voltage vector u _c on the α-axis; u _cβ is the component of the stator voltage vector u _c on the β-axis; u _eα is the component of the induced electromotive force ue on the α-axis _; u _eβ is the induced electromotive force u _e on the β-axis on the quantity.

2. Establish a discrete model of the current loop

In order to reduce the influence of electromagnetic interference on sampling, the sampling of digital control system needs to be synchronized with PWM. When using single-update (single-sampling) PWM, the sampling frequency is consistent with the switching frequency of the inverter, while when using double-update (double-sampling) PWM, the sampling frequency is twice the switching frequency of the inverter.

In the process of designing the controller, the PWM can be equivalent to a zero-order hold link, which means that the average voltage output by the inverter remains unchanged within a sampling period. The relationship between the current sampling value i(k) and the voltage input u _c (k) of the modulation link can be obtained by discretizing equation (1). The discrete state space expression is:

In the formula,

Among them, η is the integral variable; x(k) is the state variable of the discrete current loop system; _ue (k) is the sampling value of the induced electromotive force _ue in the discrete current loop system.

In the synchronous sampling mode, the output of the controller has a delay of one sampling period, that is, the control quantity calculated at kT _s needs to go through a delay of one sampling period, and at (k+1)T _s is used as the command execution link. voltage input. The delay can be expressed as:

u _c (k+1)=u(k) (3)

Combined with equations (2) and (3), the delay is included in the state space expression, and the open-loop model of the current loop control system is obtained:

Among them, x _d (k) is the new state variable matrix, and Φ _d , Γ _cd , Γ _ed and H _d are all used to represent the parameter matrix of the current-loop open-loop control system.

3. Design of current controller

In order to eliminate the steady-state error, a feedback channel including an integrator is added to the state feedback control. The corresponding control structure and integrator form are shown in Figure 1. At this time, the introduction of integral adds two integral states x _I1 (k) and x _I2 (k), and the corresponding difference equation can be expressed as:

x _I1 (k+1)=x _I2 (k) (5)

x _I2 (k+1)=-x _I1 (k)+2cos(ω ₀ T _s )x _I2 (k)+H _d x _d (k)-i _ref (k) (6)

Among them, i _ref (k) is the sampling value of the given current; ω ₀ is the angular frequency of the given current.

For ease of representation, T is introduced:

T=2cos(ω ₀ T _s ) (7)

Combined with equations (4) to (7), the integral state is added to the model, and the expression after the expansion state is obtained is:

Among them, x _a (k) is the expanded state variable matrix, and Φ _a , Γ _ca , Γ _ra and Γ _ea are used to represent the expanded parameter matrix.

From the state feedback control structure, the control law can be obtained as:

Among them, Ka is used to represent the state feedback gain matrix after the expanded state; KN _{x is} the given feedforward gain.

In the formula, the integral state x _I (k) = [x _I1 (k) x _I2 (k)] ^T ,

The original state feedback gain K=[k ₁ k ₂ ] before adding the integral state, and the integral state gain K _I =[k _I1 k _I2 ].

Among them, x _I1 (k) and x _I2 (k) are the two integration states introduced by the integrator; k ₁ and k ₂ are the gains of the original states x(k) and _uc (k) respectively; k _I1 and k _I2 are the gains for the two integration states x _I1 (k) and x _I2 (k), respectively.

Combining equations (8) and (9), the closed-loop model of the current control system can be expressed as:

In the formula, the output matrix H _a =[1 0 0 0].

Because the actual output capability of the inverter is limited, the current controller needs to have the strategy of output limiting and suppressing integral saturation. The structure is shown in Figure 2. The strategy of suppressing integral saturation adopts the inverse calculation method, and the coefficient of the inverse calculation channel is selected as the reciprocal of the feedforward coefficient.

So far, the discrete design process of the state space-based current loop proportional resonant controller has been described.

Second, the controller parameter setting method

When a first-order closed-loop system is input with a DC signal, the dynamic performance is known. At this time, the time of current regulation under the step input is directly determined by the bandwidth α _c of the system. In order to obtain similar transient performance with sinusoidal inputs, a direct zero-pole configuration is used for parameter tuning.

如图3所示。在电流控制闭环系统中，由于积分器额外引入两个极点，闭环极点有四个。来自延时的极点已经处在最佳位置，因此保持不动。为了达到期望的瞬态过程，选择由积分器引入的两个复数极点作为主导极点。最后一个实极点保持不动，并由一个零点与之相互抵消。期望的四个极点分别设置为0，

和

There are two open-loop poles of the current control system, which are introduced by the time delay and the controlled object respectively. The pole introduced by the time delay is at the origin and the pole introduced by the plant is at

As shown in Figure 3. In a current-controlled closed-loop system, there are four closed-loop poles due to the two additional poles introduced by the integrator. The pole from the delay is already in the sweet spot, so it stays put. To achieve the desired transient process, the two complex poles introduced by the integrator are chosen as the dominant poles. The last real pole remains stationary and is canceled by a zero. The desired four poles are set to 0, respectively,

and

消除实数极点。此时，主导极点为电流控制器引入的一对复极点，其位置由电流控制闭环系统的设计要求确定，如图4所示。电流控制器增益可以写成关于电流控制系统自身参数以及配置好的闭环零极点的解析式，基于此，电流控制器可进行参数自整定。As with the closed-loop poles, the two closed-loop zeros introduced by the reference feedforward should be placed reasonably. One of the zeros is set to

Eliminate the real poles. At this time, the dominant pole is a pair of complex poles introduced by the current controller, and its position is determined by the design requirements of the current control closed-loop system, as shown in Figure 4. The gain of the current controller can be written as an analytical formula about the parameters of the current control system and the configured closed-loop zero-pole. Based on this, the current controller can perform parameter self-tuning.

3. Online calculation method of controller parameters

The motor control system needs speed regulation, and the frequency of the current will change with the speed. In order to realize the current tracking without static error, the parameters of the current loop discretized proportional resonant controller must be able to be calculated online. In order to reduce the computational burden, the matrix operations in the offline calculation process need to be converted into numerical operations. The method is summarized as follows:

The approximate calculation method of the state space expression coefficient after discretization is as follows:

In the formula, F represents the coefficient -R _f /L _f , and N represents the order of the approximate calculation.

φ and τ _c can be approximately obtained from equations (11), (12) and (13).

The characteristic polynomial expected for the current control system is:

a(z)=z(z-α ₁ )(z-α ₂ )(z-α ₃ ) (14)

Among them, z is the z-transform operator; α ₁ , α ₂ and α ₃ are the other three desired closed-loop poles except at the origin.

To calculate the controller parameters, the desired characteristic polynomial (14) is expressed as:

a(z)=z ⁴ +a ₃ z ³ +a ₂ z ² +a ₁ z+a ₀ (15)

Among them, a ₀ , a ₁ , a ₂ and a ₃ are characteristic polynomial coefficients.

According to equations (14) and (15), the relationship between the characteristic polynomial coefficients and the desired closed-loop poles can be obtained:

The characteristic polynomial obtained from the current control system closed-loop model (10) is:

Among them, det represents the determinant of the matrix; I is a four-dimensional unit matrix.

Combined with equations (16) and (17), the polynomial coefficients are represented by a matrix:

Among them, M and W are used to represent the corresponding matrix.

For the convenience of calculation, formula (18) is expressed as:

Wherein, m ₁₁ ...... m ₄₄ correspond to each element in the matrix M in the expression (18); w ₁ ...... w ₄ correspond to each element in the matrix W in the expression (18).

Equation (19) shows that the state feedback gain _Ka can be obtained by matrix operation. But in order to convert matrix operations into numerical operations, first decompose the matrix M into the product of the lower triangular matrix L and the upper triangular matrix U:

Among them, l ₂₁ ...... l ₄₃ are the non-zero elements except the diagonal elements contained in the lower triangular matrix after decomposition; u ₁₁ ...... u ₄₄ are the non-zero elements contained in the upper triangular matrix after decomposition.

In the formula, the elements in the lower triangular matrix L and the upper triangular matrix U are:

Combining equations (20), (21) and (22), the elements of the matrix L and the matrix U can be calculated. From equations (19) and (20), the equation LUK _a =W holds.

Let UK _a =C, get LC=W, easily get C=L ^-1 W, let C=[c ₁ c ₂ c ₃ c ₄ ] ^T , each element of matrix C can be expressed as:

Knowing that UK _{a =} C, it is easy to obtain Ka ₌ U ^-1 C. Combining equations (21), (22) and (23), the elements of matrix Ka can be derived:

The zero-point polynomial obtained from the current control system closed-loop model (10) is:

b(z)=τ _c {KN _x z ² -(KN _x Tk _I2 )z+KN _x +k _I1 } (25)

The only unknown coefficients in the zero point polynomial are the feedforward coefficients KN _x .

In order to determine the feedforward coefficient, it is first necessary to determine the position of the closed loop zero. When designing the controller, the closed-loop zero and the pole introduced by the load are cancelled, so the position of the closed-loop zero and the pole introduced by the load is the same. At this time, the feedforward coefficient is determined by the pole introduced by the load. If the pole introduced by the load is β, the feedforward coefficient is obtained as:

KN _x =-(k _I1 +k _I2 β)/(β ² -Tβ+1) (26)

So far, the online calculation method of the current controller coefficient has been explained, and the calculation process is shown in Figure 5.

The online calculation process of current proportional resonant controller parameters is described as follows:

Start the inverter at the beginning, determine the stator resistance R _f and synchronous inductance L _f of the surface-mounted permanent magnet motor, and then calculate the discrete state space corresponding to the current loop according to the approximate numerical operation method given by equations (11) to (13). The coefficients φ and τ _c of the expression. Next, the value of the coefficient intermediate variable is calculated according to equations (18) to (22). After that, the positions of the desired closed-loop poles are determined according to the design requirements, and the matrix W is calculated according to equations (18) and (19). After obtaining the intermediate variable and matrix W, the matrix Ka is calculated according to equations (23) and (24), that is, the feedback gains k ₁ and _{k 2} of the original state and the integral state gains k _I1 and k _I2 are obtained. Determine the position of the closed-loop zero point according to the design requirements and the position of the closed-loop pole. Substitute into formula (26) to calculate the feedforward coefficient KN _x , and thus obtain all the parameters of the controller. If the on-site working conditions or other uncertain factors cause the continuous model of the permanent magnet motor current loop to change, it is necessary to return to the step of determining the stator resistance and synchronous inductance of the motor, and continue the calculation according to the original process after determining the new value. If the model does not change, determine whether the given speed of the motor has changed. If the given speed of the motor changes, go back to the step of determining the closed-loop pole position, and continue the calculation according to the original process. Whether the speed changes, until the change occurs, perform the corresponding action.

In the embodiment of the present invention, the models of each device are not limited unless otherwise specified, as long as the device can perform the above functions.

Those skilled in the art can understand that the accompanying drawing is only a schematic diagram of a preferred embodiment, and the above-mentioned serial numbers of the embodiments of the present invention are only for description, and do not represent the advantages or disadvantages of the embodiments.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (7)

1. A discretization design method for a proportional resonant controller of a permanent magnet motor is characterized by comprising the following steps:

discretizing a continuous model of a motor current loop to obtain a discrete model by considering sampling and zero-order holding characteristics of PWM in a digital control system;

under a synchronous sampling mode, the output of the controller has a delay of one sampling period, and in order to contain the delay of one sampling period in a discrete model, a state space expression is expanded to obtain an open-loop model of the current control system;

an integrator is introduced to eliminate steady-state errors, and a closed-loop model of the current control system is deduced by combining a state feedback control structure;

determining an expected zero pole of a current control closed-loop system, setting parameters of a current controller by using a direct zero pole configuration method, and determining an online parameter calculation method of the current controller according to the parameter setting method so as to meet the online parameter calculation requirement of the current controller;

the parameter setting of the current controller by using the direct zero pole configuration method specifically comprises the following steps:

the open loop poles of the current control system are two, which are respectively introduced by the time delay and the controlled object, the pole introduced by the time delay is positioned at the original point, and the pole introduced by the controlled object is positioned at the original point

R_f、L_fRespectively representing the stator resistance and the synchronous inductance of the permanent magnet motor,

selecting two plural poles introduced by the integrator as leading poles, keeping the last real pole still, and offsetting each other by a zero point; the desired four poles are each set to 0,

and

α_cis the bandwidth, ω₀Angular frequency for a given current;

one zero point is set as

Eliminating a real number pole, and determining a feed-forward coefficient of the current controller by the zero point; the dominant poles are a pair of complex poles introduced by the current controller, and the positions of the complex poles are determined by the design requirements of the current control closed-loop system.

2. The discretization design method of the proportional resonant controller of the permanent magnet motor according to claim 1, further comprising: and establishing a continuous model of the current loop of the permanent magnet motor.

3. The discretization design method of the proportional resonant controller of the permanent magnet motor according to claim 1, wherein the step of introducing an integrator to eliminate steady-state errors and the step of deducing a closed-loop model of a current control system by combining a state feedback control structure specifically comprises the steps of:

a feedback channel comprising an integrator is added in the state feedback control, and two integration states are added by introducing integration to obtain a corresponding difference equation;

adding the integral state into a differential equation to obtain an expression in an expanded state;

and obtaining a control law by the state feedback control structure, and further deducing a closed-loop model of the current control system.

4. The discretization design method of the proportional resonant controller of the permanent magnet motor according to claim 3, wherein the corresponding differential equation is as follows:

x_I1(k+1)＝x_I2(k)

x_I2(k+1)＝-x_I1(k)+2cos(ω₀T_s)x_I2(k)+H_dx_d(k)-i_ref(k)

wherein i_ref(k) Sampling a given current value; x is the number of_I1(k)、x_I2(k) Two integration states introduced for the integrator; h_dA parameter matrix for representing a current loop open loop control system; x is the number of_d(k) Is a new state variable matrix.

5. The discretization design method of the proportional resonant controller of the permanent magnet motor according to claim 4, wherein the expression after the expansion state is specifically as follows:

wherein x is_a(k) Is the expanded state variable matrix, phi_a、_ca、_raAnd_eaare all used to represent the parameter matrix after expansion, phi_d、_cd、_edAll used for representing the parameter matrix of the open-loop control system of the current loop; t2 cos (ω)₀T_s)，u_e(k) Inducing an electromotive force u in a system for discrete current loops_eThe sampling value of (2);

the control law is as follows:

K_a＝[K K_I]，

wherein, K_aA state feedback gain matrix for representing the expanded state; KN_xFor a given feedforward gain, the integration state x_I(k)＝[x_I1(k) x_I2(k)]^T；

Adding the original state feedback gain K before the integral state to K₁k₂]Integral state gain K_I＝[k_I1k_I2]，k₁、k₂Respectively in original states x (k) and u_c(k) A gain of (d); k is a radical of_I1、k_I2Respectively two integration states x_I1(k) And x_I2(k) The gain of (c).

6. The discretization design method of the proportional resonant controller of the permanent magnet motor according to claim 5, wherein the closed-loop model of the current control system is as follows:

x_a(k+1)＝(Φ_a-_caK_a)x_a(k)+(_ra+_caKN_x)i_ref(k)+_eau_e(k)

i(k)＝H_ax_a(k)

in the formula, output matrix H_a＝[1 0 0 0]。

7. The discretization design method for the proportional resonant controller of the permanent magnet motor according to any one of claims 1-6, wherein the method further comprises the following steps:

the current controller gain can be written into an analytic expression about the current control system parameters and the configured closed loop pole zero, and based on the analytic expression, the current controller can perform parameter self-tuning.

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